Context and background: Complex fuzzy theory has a strong practical implication in many real-world applications. Complex Fuzzy Inference System (CFIS) is a powerful technique to overcome the challenges of uncertain, periodic data. However, a question is raised for CFIS: How can we deduce and predict the result in case there is little knowledge about data information and rule base? This is significance because many real applications do not have enough knowledge of rule base for inference so that the performance of systems may be low. Thus, it is necessary to have an approximate reasoning method to represent and derive final results. Motivation: Recently, the Mamdani Complex Fuzzy Inference System (M-CFIS) has been proposed with a specific inference mechanism according to the Mamdani type. A new improvement so-called the Mamdani Complex Fuzzy Inference System with Rule Reduction (M-CFIS-R) has been designed to utilize granular computing with complex similarity measures to reduce the rule base so as to gain better performance in decision-making problems. However in M-CFIS-R, testing data are checked by matching with each rule in the rule base, which leads to a high cost of computational time. Besides, if the testing data contain records that are not inferred by the rule base, the output cannot be generated. This happens in real commerce systems in which the rule base is small at the time of creation and needs to feed with new rules. Methodology: In order to handle those issues, this paper first time proposes the Fuzzy Knowledge Graph to represent the rule base in terms of linguistic labels and their relationships according to the rule set. An adjacent matrix of Fuzzy Knowledge Graph is generated for inference. When a record in the Testing dataset is given, it would be fuzzified and labelled. Each component in the record is checked with the Fuzzy Knowledge Graph by the inference mechanism in approximate reasoning called Fast Inference Search Algorithm. Then, we derive the label of the new record by the Max-Min operator. Besides, we also propose four extensions of Mamdani Complex Fuzzy Inference System Rule Reduction including Sugeno Complex Fuzzy Inference Systems, Tsukamoto Complex Fuzzy Inference Systems, Complex Fuzzy Measures and Complex Fuzzy Integrals in M-CFIS-R. Results: The experiments on the UCI Machine Learning datasets show that the proposed method classifies samples as correctly as M-CFIS-R with very lower run time (6.45 times on average). The experiments are performed through many tests via 2 main scenarios. Conclusion: The proposed system has good performance in reducing the computational time of inference with acceptable accuracy. It has ability to work with systems having limited knowledge and rule base.

Complex fuzzy theory has strong practical background in many important applications, especially in decision-making support systems. Recently, the Mamdani Complex Fuzzy Inference System (M-CFIS) has been introduced as an effective tool for handling events that are not restricted to only values of a given time point but also include all values within certain time intervals (i.e., the phase term). In such decision-making problems, the complex fuzzy theory allows us to observe both the amplitude and phase values of an event, thus resulting in better performance. However, one of the limitations of the existing M-CFIS is the rule base that may be redundant to a specific dataset. In order to handle the problem, we propose a new Mamdani Complex Fuzzy Inference System with Rule Reduction Using Complex Fuzzy Measures in Granular Computing called M-CFIS-R. Several fuzzy similarity measures such as Complex Fuzzy Cosine Similarity Measure (CFCSM), Complex Fuzzy Dice Similarity Measure (CFDSM), and Complex Fuzzy Jaccard Similarity Measure (CFJSM) together with their weighted versions are proposed. Those measures are integrated into the M-CFIS-R system by the idea of granular computing such that only important and dominant rules are being kept in the system. The difference and advantage of M-CFIS-R against M-CFIS is the usage of the training process in which the rule base is repeatedly changed toward the original base set until the performance is better. By doing so, the new rule base in M-CFIS-R would improve the performance of the whole system. Experiments on various decision-making datasets demonstrate that the proposed M-CFIS-R performs better than M-CFIS.

Dynamic multi-criteria decision-making (DMCDM) models have many meaningful applications in real life in which solving indeterminacy of information in DMCDMs strengthens the potential application of DMCDM. This study introduces an extension of dynamic internal-valued neutrosophic sets namely generalized dynamic internal-valued neutrosophic sets. Based on this extension, we develop some operators and a TOPSIS method to deal with the change of both criteria, alternatives, and decision-makers by time. In addition, this study also applies the proposal model to a real application that facilitates ranking students according to attitude-skill-knowledge evaluation model. This application not only illustrates the correctness of the proposed model but also introduces its high potential appliance in the education domain.

Decision-making activities are prevalent in human life. Many methods have been developed to address real-world decision problems. In some practical situations, decision-makers prefer to provide their evaluations over a set of criteria and weights. However, in many real-world situations, problems include a lack of weight information for the times, criteria, and decision-makers (DMs). To remedy such discrepancies, an optimization model has been proposed to determine the weights of attributes, times, and DMs. A new concept related to the correlation measure and some distance measures for the dynamic interval-valued neutrosophic set (DIVNS) are defined in this paper. An extend Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method in the interval-valued neutrosophic set with unknown weight information in dynamic neutrosophic environments is developed. Finally, a practical example is discussed to illustrate the feasibility and effectiveness of the proposed method.